(a^3+b^3)-(a^2b+ab^2)
=a^3-a^2b+b^2-ab^2
=a^2(a-b)-b^2(a-b)
=(a^2-b^2)(a-b)
=(a+b)(a-b)^2
a>0,b>0,所以a+b>0
(a-b)^2>=0
所以(a+b)(a-b)^2>=0
所以a^3+b^3>=a^2b+ab^2
當(dāng)a=b時(shí)取等號(hào)